Years 11–12 · Week 9 of 12
Quantum Teleportation
Learning goals
By the end, you can…
- Identify the input qubit, shared Bell pair, measurements and corrections in teleportation.
- Trace the protocol in circuit order using a stated classical-bit convention.
- Explain why two classical bits and pre-shared entanglement are both required.
- Connect teleportation with no-cloning and no faster-than-light communication.
What you already know
Connect to a familiar idea
Entanglement creates joint correlations but cannot by itself transmit a controlled message. Teleportation combines entanglement, local gates, measurement and classical communication to reconstruct a state elsewhere.
- Bell-state preparation
- CNOT, H, X and Z gates
- Computational-basis measurement and state update
Opening story
Start with something familiar
Suppose Alice must transfer a fragile preparation to Bob, but direct transport is unavailable. The teleportation protocol does not move the particle. It consumes a shared entangled pair and sends two ordinary bits so Bob can transform his qubit into the original state.
Plain-English explanation
Build the idea carefully
Resources and circuit steps
Alice holds an input |ψ⟩ = α|0⟩ + β|1⟩ and one half of a Bell pair; Bob holds the other half. The Bell pair must have been distributed before the protocol begins. Alice applies CNOT from the input to her Bell-pair qubit, then H to the input. She measures both of her qubits, obtaining two ordinary classical bits m₀ and m₁. These results are random and must be sent to Bob.
Corrections, no-cloning and communication limits
With the convention m₀ = input-qubit result and m₁ = Alice's Bell-qubit result, Bob applies Z when m₀ = 1 and X when m₁ = 1. The four branches 00, 01, 10 and 11 therefore require I, X, Z and ZX up to an irrelevant global phase, leaving Bob's qubit in |ψ⟩. Alice's measurements remove the original independent copy, consistent with the no-cloning theorem. Bob cannot reconstruct |ψ⟩ until the two classical bits arrive, so teleportation neither moves matter nor sends usable information faster than light.
Try the model
Teleportation circuit animator
Choose an input state, then pause or step through Bell-pair preparation, Alice's gates, both measurements, classical communication and Bob's corrections.
Qubit 0 is the least-significant state-vector bit. Displayed basis labels read q(n−1)…q0.
Ready. Adjust a control, then run the model.
What this model shows: The animation transfers a state in an ideal simulator. It does not teleport a person, object or particle.
Text alternative for this interactive
Text alternative: outcome 00 needs I, 01 needs X, 10 needs Z and 11 needs both Z and X under the stated m₀m₁ convention.
Expected observation: Before Bob receives m₀ and m₁ his local state does not reveal |ψ⟩; after the corresponding X and Z corrections, his state matches the input.
Guided activity
Trace all four measurement branches
- Choose a symbolic input α|0⟩ + β|1⟩.
- Complete the four-row table for m₀m₁ = 00, 01, 10 and 11.
- Record Bob's pre-correction state and required correction in each row.
- Explain why Alice no longer retains an independent |ψ⟩ after measurement.
Evidence to collect: A correct four-branch correction table and a written explanation that the protocol consumes the original state and requires classical communication.
Glossary
Words to know
- quantum teleportation
- A protocol that transfers a quantum state using entanglement and classical communication.
- Bell pair
- A shared pair of qubits prepared in a Bell state.
- classical bit
- An ordinary recorded value, 0 or 1, sent through a classical channel.
- conditional correction
- A gate applied according to a received measurement bit.
- no-cloning theorem
- The result that an arbitrary unknown quantum state cannot be copied perfectly.
- classical channel
- A communication path carrying ordinary classical information.
- global phase
- A common phase factor that does not change physical predictions.
Short recap
Keep these ideas
- Teleportation starts with an unknown input and a pre-shared Bell pair.
- Alice's two measurements produce two classical bits.
- Bob uses those bits to select X and Z corrections.
- The protocol transfers a state, not matter, and creates no faster-than-light signal or extra copy.
Knowledge check
7 clear questions
Choose an answer for immediate feedback. You may retry, and your best submitted score is kept.
Mathematical Extension Optional extension for Year 12
Expand the three-qubit state immediately before Alice's measurements and group terms by her two-bit outcomes. Show that Bob's conditional states are |ψ⟩, X|ψ⟩, Z|ψ⟩ and XZ|ψ⟩ up to the chosen bit order and global phase.
Try this
Choose |ψ⟩ = (3|0⟩ + 4|1⟩)/5. For each measurement branch, apply the stated correction matrix and verify that Bob's final probabilities are 9/25 and 16/25.
Adult support Teacher and parent notes
Discuss
- Which resources must exist before Alice begins?
- Why can Bob not use his qubit before the classical bits arrive?
- Where in the protocol is the original independent state lost?
Answer guidance
Correction tables vary with wire and bit-string conventions. Accept a different table only when the student states a consistent convention and derives all branches correctly.
Offline activity
Use three wire strips, gate cards and four classical outcome cards. Students physically trace each branch and place the matching correction.
Safety
Avoid science-fiction imagery of people disappearing or claims of instant transmission. The simulator contains no real hardware connection.
Sources and further reading
Checked references for this lesson
These sources support the lesson’s main scientific claims. Links open on the source organisation’s site.
- Basics of Quantum Information IBM Quantum Learning · official course · checked 2026-08-02
- Entanglement and correlations Microsoft Learn · official documentation · checked 2026-08-02
- Quantum Computation and Quantum Information Cambridge University Press · textbook publisher page · checked 2026-08-02
Content review: Reviewed on 2026-08-02.